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Investment advice and corporate finance
Module 12Investment Management and Corporate FinanceA portfolio holds 60% in Fund A (standard deviation 20%) and 40% in Fund B (standard deviation 30%). The correlation between their returns is 0.25. What is the portfolio standard deviation?
σp² = wA²σA² + wB²σB² + 2wAwBρσAσB = 0.36(0.04) + 0.16(0.09) + 2(0.6)(0.4)(0.25)(0.20)(0.30) = 0.0144 + 0.0144 + 0.0072 = 0.0360, so σp = √0.0360 = 18.97%. Dropping the covariance term (as if ρ = 0) gives √0.0288 = 16.97%. Forgetting the 2 in front of the covariance term gives √0.0324 = 18.00%. The weighted average of the standard deviations, 0.6(20%) + 0.4(30%) = 24.00%, holds only when ρ = +1; with ρ below 1, diversification pulls risk below that average. Source: SIDC M12 Study Outline Topic 6.2 Markowitz Portfolio Theory; Bodie, Kane and Marcus, Investments, chapter 'Optimal Risky Portfolios'; CFA Institute, Portfolio Risk and Return: Part I (2026 Level I) (as at October 2026).
Taking the weighted average of the two standard deviations, which assumes perfect positive correlation.
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